Lifting paths on quotient spaces
type: Item
instance of: scholarly article
title: Lifting paths on quotient spaces
zbMATH Open document ID: 1168.54014
author: J. Martínez
published in: Topology and its Applications
publication date: 2009-05-28T00:00:00Z
review text: The classical Hahn-Mazurkiewicz Theorem asserts that a metric continuum is the continuous image of the closed unit interval \([0,1]\) if and only if it is locally connected. In the non-metric case, the situation turns out to be quite complicated. The authors consider the following problem. Let \(X\) be a compactum and \(G\) an upper semi-continuous decomposition of \(X\) such that each element of \(G\) is the continuous image of an ordered compactum. If the quotient space \(X/G\) is the continuous image of an ordered compactum, under what conditions is \(X\) also the continuous image of an ordered compactum? The authors give some examples to show that one must place severe conditions on \(G\) if one wishes to obtain positive results. They prove that the compactum is the image of an ordered compactum when each \(g\in G\) has \(0\)-dimensional boundary. They also consider the case when \(G\) has only countably many non-degenerate elements.
reviewed by: Alejandro Illanes
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54C05
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 5558964
zbMATH Keywords: decomposition
zbMATH Keywords: lifting images of arcs
zbMATH Keywords: locally connected continuum
zbMATH Keywords: ordered continuum
zbMATH Keywords: null family
MaRDI profile type: Publication
full work available at URL: j.topol.2009.02.005
OpenAlex ID: W1973924943
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DOI: 10.1016/J.TOPOL.2009.02.005
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description: scientific article; zbMATH DE number 5558964